00 IA ε-n I,, 3, 4, 5, 6, 7, 8, 9 4 6 ε-n ε-n ε-n? {a } = {a } = a a {a } = ε ε N N a a < ε
ε-n ε ε N a a < ε N ε ε N ε N N ε N [ > N = a a < ε] ε > 0 N N N ε N N ε N N ε a = lim a = 0
ε-n 3 ε N 0 < ε N ε N [ > N = ] 0 < ε ε ε ε N ε ε N ε = 0. N ε = 0.0 N ε ε N ε N ε N ε ε ε 0 ε ε 0 ε ε 0 ε ε ε 0 [ > N = a a < ε 0 ] N N ε 0 N {a } = a =, a = 0 a a < ε 0 < ε 0
ε-n 4 > ε 0 a 0 < ε 0 N ε 0 N N ε 0 N N ε ε N N ε 0 [ ] N = + ε 0 ε N. ε N N = [ ] + ε a [a] a [ ] + > ε ε N < N = [/ε] + < /ε = ε < ε 0 = lim = 0 ε N [ > N = a a < ε] N
ε-n 5 ε N > N = a a < ε a x + 3 = a x a x [x + 3 = a] x = a 3 r r < a = r lim a = 0 ε ε ε 0 ε 0 N a 0 < ε 0 N N {a } = a 0 = r 0 = r = r r r < ε 0 r = 0 r = 0 < ε 0 N r = 0 0 < r < s r = = + s (s > 0) r ( + s) = + s + ( ) s + + s + s
ε-n 6 s > 0 ( + s) = + s + ( ) s + + s + > s r < s s < ε 0 r < ε 0 N N > sε 0 N N N ε N ε ε N {a } = {a } = N s N N N. ε r = 0 a = 0 a 0 = 0 < ε lim a = 0 r 0 s N r = + s N > sε s ( + s) = + s + N a 0 = r = ( ) s + + s + s > s ( + s) < s < sε s = ε lim a = 0
ε-n 7 3 a a = a lim a = 0 a = 0 a 0 ε ε 0 ε 0 N a 0 = a < ε 0 N ε 0 N {a } = {a } = N a 0 = a = a a < ε 0 ε 0 a a = a a a a a a < a! a! ( ) a ( ) a < ε 0 a a! ( ) a <! ε 0 () N N a <
ε-n 8 > N () N N ε 0 r < lim r = 0 N () N lim r = 0 N N. a a lim = 0 < ε N N! ε ( ) a 0 = a < a a = <!!!! ε = ε lim a = 0 lim = 0 ε N ε N? ε N [ > N = [ > N = [ > N = < ε] <! ] ε < ε] ε! ε?
ε-n 9 ε N [ > N = a ] < ε ε N [ ε N > N = < ε] (3) ε N 3. () ε ε 0. ε 0! (3) ε 3. (3). ε N 4. N () N > N = a < ε 0 4 lim (a + b ) = lim a + lim b a < a! ( ) a ε-n? A () 4 :,,3 ε N [ > N = c c < ε] (4)
ε-n 0 ε N ε N [ > N = a c < ε] (5) ε N [ > N = b c < ε] (6) (5) (6) ε ε (4) ε (4) ε ε 0 ε ε 0 (5),(6) ε N N N N c c < ε 0 N c c < ε (5) (6) c = a + a + c < ε 0 (5) (5) ε ε 0 (5) N N a + > N a c = b b c < ε 0 (6) (6) ε ε 0 (6) N N b c c < ε 0 > N b [ > N a ] [ > N b ]
ε-n N > N c c < ε 0 N > N a > N b c c < ε 0 N a N b N N = max{n a, N b } N N N a N b N a N b 5 : 4 {a } = a {b } = b c = a + b {c } = a + b ε N [ > N = (a + b ) (a + b) < ε] ε N [ > N = a a < ε] ε N [ > N = b b < ε] ε ε 0 ε 0 > N (a + b ) (a + b) < ε 0 N (a + b ) (a + b) < ε 0 a + b a + b (a + b ) (a + b) = (a a) + (b b) a a + b b a a + b b < ε 0 (7)
ε-n a a b b (7) (7) (7) a a b b ε 0 ε 0 ε 0 a a < ε 0 b b < ε 0 a a < ε 0 ε ε0 N N a > N a b b < ε0 ε ε 0 N N b > N b N a N b a a < ε0 b b < ε 0 a a + b b < ε 0 (a + b ) (a + b) < ε 0 N N a N b max{n a, N b } N (a + b ) (a + b) < ε 0 ε 0 a a < ε 0 b b < ε 0 ε 0 a a < ε 0 b b < ε 0 (a + b ) (a + b) a a + b b < ε 0 < ε 0 < ε 0 ε 0 a a b b ε 0 ε 0 < ε 0 < ε 0 6 : 4 4 [ ε N > N = a + a + + a ε N [ > N = a a < ε] ] a < ε
ε-n 3 ε ε 0 ε 0 N a + a + + a a < ε 0 N ε-n a a a a a a ε-n a k a a +a + +a k a + a + + a a = a + a + + a a = (a a) + (a a) + + (a a) a + a + + a a a a + a a + + a a ε 0 a a a a ε 0 ε 0 a k a < ε 0 k k a k a k a k a ε 0 a k a < ε 0 a k a < ε 0 a k a < ε 0 a k a ε 0 ε ε 0
ε-n 4 N N a a a < a a + + a N a a + + a N a a = a a + + a Na a + a N a + a + ε 0 + + ε 0 + N a ε 0 + + a a > N a N a < = N a ε 0 < ε 0 N a ε 0 a a + a a + + a Na a a a + a a + + a Na a N N a a,..., a Na a N N > N a ε 0 < ε 0 N N a a + a + + a a < ε 0 + ε 0 = ε 0 < ε 0 < ε 0 ε 0 ε ε 0 ε ε 0 ε0 k > N a = a k a < ε 0 N a a a,..., a N a a N > N a ε 0 / N N N a a + a + + a a < ε 0 + ε 0 = ε 0
ε-n 5 4